arXiv:2609. 12590v1 Announce Type: cross Abstract: We investigate the stochastic-gradient query complexity of sampling smooth strongly log-concave distributions in any fixed Euclidean dimension.
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called \emph{smoothed Picard Hamiltonian Monte Carlo}, which combines Gaussian smoothing, Picard iteration, an...
arXiv:2607. 28413v1 Announce Type: cross Abstract: Let $\mu(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $\kappa=L/m$ the condition number.
arXiv:2609.06905v1 Announce Type: cross Abstract: We study the problem of sampling from $\mu(\mathrm{d}x)\propto e^{-V(x)}\,\mathrm{d}x$ on $\mathbb{R}^d$, where $V$ is $\alpha$-strongly convex and $...
arXiv:2607. 12902v1 Announce Type: cross Abstract: We show the Randomized Hamiltonian Monte Carlo (RHMC) algorithm has accelerated mixing time guarantees for sampling from log-concave probability distributions.
We show the Randomized Hamiltonian Monte Carlo (RHMC) algorithm has accelerated mixing time guarantees for sampling from log-concave probability distributions. RHMC proceeds by repeatedly simulating the continuous-time Hamiltonian dynamics for some random integration times, and resetting the velocity to be an independent Gaussian random variable between each simulation.
arXiv:2609.15268v1 Announce Type: new Abstract: We revisit Valiant's algorithm (Commun. ACM'84) for learning $n$-variable CNF formulas with clause size $k$ and variable degree $d$ from i.i.d. uniform...
arXiv:2509.26175v2 Announce Type: replace Abstract: The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov chain Monte Carlo method for sampling from high-dimensional distributions when...
arXiv:2603. 25622v2 Announce Type: replace-cross Abstract: We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition.
The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.